## Bidirectional Learning for Offline Infinite-width Model-based Optimization

### Can Chen · Yingxueff Zhang · Jie Fu · Xue (Steve) Liu · Mark Coates

##### Hall J #234

Keywords: [ infinite-width neural network ] [ offline model-based optimization ] [ Neural Tangent Kernel ] [ Out-of-Distribution ] [ bi-level optimization ]

[ Abstract ]
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Thu 1 Dec 9 a.m. PST — 11 a.m. PST

Abstract: In offline model-based optimization, we strive to maximize a black-box objective function by only leveraging a static dataset of designs and their scores. This problem setting arises in numerous fields including the design of materials, robots, DNAs, proteins, etc. Recent approaches train a deep neural network (DNN) model on the static dataset to act as a proxy function, and then perform gradient ascent on the existing designs to obtain potentially high-scoring designs. This methodology frequently suffers from the out-of-distribution problem where the proxy function often returns adversarial designs. To mitigate this problem, we propose $\textit{\textbf{B}i\textbf{D}irectional learning for offline \textbf{I}nfinite-width model-based optimization}~(\textbf{BDI})$. BDI consists of two mappings: the forward mapping leverages the static dataset to predict the scores of the high-scoring designs, and the backward mapping leverages the high-scoring designs to predict the scores of the static dataset. The backward mapping, neglected in previous work, can distill more information of the static dataset into the high-scoring designs, which effectively mitigates the out-of-distribution problem. Yet, for a finite-width DNN model, the loss function of the backward mapping is intractable and only has an approximate form, which leads to a significant deterioration of the design quality. We thus adopt an infinite-width DNN model and propose to employ the corresponding neural tangent kernel to yield a closed-form loss for more accurate design updates. Experiments on various tasks verify the effectiveness of BDI. The code is available [here](https://github.com/GGchen1997/BDI).

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